The Mathematics of Seeing Clearly: Deblurring Images for National Security

A blurred image is often only a minor nuisance to photographers and everyday social media enthusiasts. But as Derek Jung learned as a graduate student intern in the National Science Foundation’s (NSF) Mathematical Sciences Graduate Internship (MSGI) Program, a blurry image becomes much more serious in the context of national security. Research designed to deblur images is vitally important to national security efforts, which attempt to identify unknown sensitive materials captured in photographs. Jung, a mathematics doctoral student at the University of Illinois at Urbana-Champaign, was tasked with finding a solution to deblur images.

The MSGI Program provides research opportunities and hands-on experience in the application of mathematics in nonacademic settings for Ph.D. students via internships at federal national laboratories, industries, and other facilities.

“I do mathematics because it helps me grow personally and build relationships,” Jung said, reflecting on his decision to pursue the subject. “I’m allowed to think for hours about a problem, take regular walks around campus, and I’m apparently doing my job! Solving a problem leads to pride and self-confidence, while toiling for months is accompanied by support from my peers and family.”

While appointed to the Nevada National Security Site’s Signal Processing and Applied Mathematics team north of Las Vegas, Jung integrated his mathematics background with an industry environment for the first time. To develop a solution for deblurring images, he first sought to understand how they become blurred. With the help of mentors Aaron Luttman and Kevin Joyce, Jung investigated model theories about the functioning of blurred images and attempted to prove their functionality with math. He based his research on measure theory, functional analysis, and harmonic analysis — all forms of advanced calculus that seek to describe spaces.

Focusing on key gaps in existing research, Jung made significant contributions that will soon be ready for publication. He continued to pursue new ideas to clarify blurry images after his return to the University of Illinois. When presenting his research to colleagues, Jung received a fresh perspective and suggestion, which he used to devise a solution to the last remaining gaps in the problem. His successful research contributes to efforts to find and identify sensitive materials, thus advancing national security.

“Before this summer internship, I never had experience in applying mathematics to the real world,” Jung said. “My background was pure mathematics, and I thought it would be difficult to find an opportunity to apply my skills in an industry setting. The experience was spectacular and unique; it was unbelievable how the NSF’s MSGI Program set me up with a project and location that enabled me to contribute and feel comfortable.”

Luttman, Joyce, and Jung plan to submit their research to the Journal of Mathematical Analysis and Applications. Jung expects to receive his doctorate in 2019 and hopes to begin a postdoctoral position. He would eventually like to teach at a university or conduct research at a federal laboratory.

Jung was among 40 doctoral students to benefit from the NSF’s MSGI Program, all of whom were awarded spots for 10 weeks at federal laboratories, industry-based locations, and other approved facilities. Funded by the NSF, the The MSGI Program is administered through the U.S. Department of Energy’s (DOE) Oak Ridge Institute for Science and Education (ORISE).

Erik Palmer of the University of South Carolina was inspired to pursue opportunities within the national laboratory system during a local SIAM student chapter talk. While stationed at Lawrence Berkeley National Laboratory, Palmer contributed to efforts to improve understanding of multiphase flows — the movement of materials with different states or phases. Multiphase flow research is used in a variety of applications, including advancing clean and efficient energy, delivering more precise medical therapies, and optimizing waste treatments.

At Lawrence Livermore National Laboratory, Benie Justine N’Gozan of the University of Texas, Arlington spent her time developing new statistical learning algorithms to interpret complex machine learning models. Her research helps improve machine learning models—used widely in areas such as business and healthcare—that predict future events.

Steven Reeves of the University of California, Santa Cruz spent his time at Lawrence Berkeley adapting an existing cosmology simulation code to incorporate the influence of magnetic fields. The code, which is run on some of the world’s largest supercomputers, is used to simulate the formation of structures throughout the universe.

To find out more about these experiences and further opportunities in STEM, visit the ORISE website. ORISE supports the DOE and other federal agencies’ missions to strengthen the nation’s science education and research initiatives. ORISE is managed for the DOE by Oak Ridge Associated Universities. Applications are now open for the NSF’s 2018 MSGI Program.

Annette Hilton holds a bachelor’s degree in geology and is currently employed as an intern in the Scientific Assessment and Workforce Development unit of Oak Ridge Associated Universities (ORAU). Amanda Freuler received her bachelor’s degree in mass communication from Middle Tennessee State University. She currently serves as ORAU’s Communications and Marketing intern.